Weak Charge Quantization on Superconducting Islands

TL;DR

This paper investigates how quantum fluctuations and Andreev transport affect charge quantization in a superconducting quantum dot, revealing exponential renormalization of charging energy through instanton and RG methods.

Contribution

It introduces a combined instanton and functional RG approach to analyze charge fluctuations and renormalization in superconducting quantum dots with complex interfaces.

Findings

Quantum fluctuations cause exponential renormalization of charging energy.

Both instanton and RG methods yield consistent results.

Derived renormalization in terms of multi-channel transmission matrices.

Abstract

We consider the Coulomb blockade on a superconductive quantum dot strongly coupled to a lead through a tunnelling barrier and/or normal diffusive metal. Andreev transport of the correlated pairs leads to quantum fluctuations of the charge on the dot. These fluctuations result in exponential renormalization of the effective charging energy. We employ two complimentary ways to approach the problem, leading to the coinciding results: the instanton and the functional RG treatment of the non-linear sigma model. We also derive the charging energy renormalization in terms of arbitrary transmission matrix of the multi-channel interface.